Edit armature with existing animations
Editing armature with existing animations is totally possible.

When you edit the armature in edit-mode, you directly change the rest-position. Any transformation (animation) is relative to this rest-position, so by changing the rest-pose you might break the animation (but if the animation is mostly rotations and you change only proportions of bones there should be no problem) 

The rest-position is identical to pose-position without any transformations or constraints. This is by definition, so when you Alt + G, Alt + R, and Alt + S, and you turn off all constraints you must get the rest-position.

You can also apply any pose as a rest-position by Pose > Apply > Apply Pose As Rest Pose. How to do that with already binded mesh is here: Can I set my pose position like the new rest position?

Any animation can be also edited so it is not ruined:
How do I resize an armature without ruining its poses?